Frames and Arrows are the beginning of a Function Table.
The student is applying the "rule." To me the big important idea is the fact that the number is "changing" to fit the rule or mathematicians would say that they have a relationship.
So when I introduce the rule, I start be making it a concrete experience.
I start with a large mat that I traced onto a piece of vinyl fabric or rolled bulletin board paper, using an overhead projector. This is the image that is traced:
The student steps on the mat at the "In" and is wearing a coat. The rule is: Add 1 mitten.
Therefore, when they step out of the rule box they now have a coat + 1 mitten on.
The next student steps into the rule box one the "In" and is given the rule. The rule is: Add 1 hat.
Therefore, when they step out of the rule box they now have a coat + 1 hat.
A Class discussion follows ABOUT HOW THE RULE EFFECTS THE STUDENT WHEN THEY ENTER THE IN AND EXIT THE OUT. The effect is not always the same.
Next, I have the student with the coat + 1 mitten enter the "In" and receive the +1 mitten rule. I ask the students to predict what will happen when the student steps "Out" of the box.
The student will have 1 coat and 2 mittens.
The next student with 1 coat + 1 Hat enters into the box and receives the rule +1 mitten.
Next, the students predict what will happen.
The student will have 1 coat, 1 hat, and 1 mitten.
Now introduce a mat that looks like this:
The rule is add 1 mitten.
Begin by drawing a picture of 1 mitten over the top of each arrow.
Student stands on the first box with 0 mittens.
The second box= student with 1 mitten.
The third box = student with 2 mittens.
The fourth box = student with 3 mittens.
The last box = student with 4 mittens.
Next make the rule +2
Begin by drawing "+2" over the top of each arrow.
Student stands on the first box with a dry erase board on which you have written "3".
The second box = erase 3 and write the number 5.
Ask the students why they think that you changed the number from 3 to 5.
The third box = erase 5 and write the number 7.
Ask the students why they think that you changed the number from 5 to 7.
(You applied the rule of +2 )
Continue onto the fourth and fifth boxes.
Now you have taken an abstract template and made it understandable to your students.
In First Grade, you might leave the words "in and out," or if your students are ready, you can add...
input and output
So what do you think about my idea to make the frames and arrow template more understandable?
Please share your thoughts.